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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 398 · 40 questions
TalentJR

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

NameDateTime takenScore ___ / 40
  1. 1.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 68? (a) 8 (b) 6 (c) 7 (d) 5
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 9 (b) 6 (c) 7 (d) 8
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 18 (b) 19 (c) 7 (d) 17
  5. 5.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 528 (c) 538 (d) 537
  6. 6.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 11 (d) 8
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 3 (b) 15 (c) 13 (d) 14
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 9 (b) 7 (c) 6 (d) 8
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 9 (b) 20 (c) 19 (d) 18
  10. 10.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  11. 11.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 76? (a) 8 (b) 5 (c) 6 (d) 7
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 20 (b) 8 (c) 18 (d) 19
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 15 (b) 4 (c) 14 (d) 16
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 15 (b) 17 (c) 16 (d) 5
  16. 16.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 592 (b) 582 (c) 466 (d) 591
  17. 17.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 114 (c) 105 (d) 106
  18. 18.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 21 (c) 7 (d) 63
  19. 19.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 61 (c) 62 (d) 52
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 9 (b) 19 (c) 21 (d) 20
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 14 (b) 16 (c) 5 (d) 15
  22. 22.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 298 (c) 270 (d) 297
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 3 (b) 5 (c) 4 (d) 2
  24. 24.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 60 (c) 180 (d) 20
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 58? (a) 6 (b) 5 (c) 4 (d) 7
  26. 26.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 17 (c) 153 (d) 54
  27. 27.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 125 (c) 134 (d) 116
  28. 28.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 8 (d) 11
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 15 (b) 13 (c) 14 (d) 3
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 93? (a) 20 (b) 18 (c) 9 (d) 19
  31. 31.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 10 (d) 5
  32. 32.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 374 (b) 444 (c) 454 (d) 453
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 74? (a) 16 (b) 18 (c) 7 (d) 17
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 74? (a) 7 (b) 5 (c) 8 (d) 6
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 17 (b) 7 (c) 19 (d) 18
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 15 (b) 3 (c) 14 (d) 13
  37. 37.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 57 (c) 60 (d) 19
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 44? (a) 5 (b) 2 (c) 3 (d) 4
  39. 39.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 11 (c) 36 (d) 33
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 8 (b) 9 (c) 6 (d) 7

Answer key

  1. 4
  2. 7
  3. 8
  4. 18
  5. 537
  6. 9
  7. 14
  8. 8
  9. 19
  10. 3
  11. 3
  12. 7
  13. 19
  14. 15
  15. 16
  16. 591
  17. 105
  18. 21
  19. 61
  20. 20
  21. 15
  22. 297
  23. 4
  24. 60
  25. 6
  26. 51
  27. 125
  28. 9
  29. 14
  30. 19
  31. 4
  32. 453
  33. 17
  34. 7
  35. 18
  36. 14
  37. 57
  38. 4
  39. 33
  40. 8

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